List of Divisibility Rules
For explanation of general divisibility rules explained, see Divisibility Rules. For Mobile Devices, it is strongly recommended to view this page in "PC mode", or simply view the Divisibility Rules page above. Below is a List of Divisibility Rules sorted by number. Difficulty Coding Additionally, if an alternative method is available (albeit it would be hard most of the time), the description for that number has a pink background. Divisibility of Numbers below 5 |simpex=4,623 is divisible by one; 91,237 is divisible by one. }} |simpex=65,156,151,594 is divisible by two because the units digit is 4, and 1,597,534,568,852 is divisible by two because the units digit is 2. }} |simpex=Is 12423 divisible by 3? (1) Add all the digits together, we get 1 + 2 + 4 + 2 + 3 = 12. (2) 12 is divisible by 3, so 12423 is, too. |adv=''The advanced method is a lot less efficient. '' Trim the rightmost digit. Add the digit to the rest of the number. |advex=Is 12423 divisible by 3? (1) Trim off the rightmost digit, 3. Add it to 1242. 1242 + 3 = 1245. (2) Repeat the steps: 124 + 5 = 129. 12 + 9 = 21. 2 + 1 = 3. }} |simpex=156,128 is divisible by four, and 6,416 is divisible by four. The last two digits are 28 and 16, respectively, both of which are divisible by 4. |adv=Alternatively, add 2 times the tens digit to the ones digit, then check the divisibility. |advex=For 156,128, 2 x 2 + 8 = 12. 12 is divisible by 4. Therefore, 156,128 is divisible by 4. }} |simpex=213,478,765 is divisible by 5 because the last digit is 5. }} Divisibility of Numbers between 6 and 10 Another strategy is to add 5 times the last digit to the remaining digits instead. |simpex=Is 3,409 is divisible by 7? First, take 9 from 3409, and multiply 9 by 2 (9*2=18). Then, subtract the doubled digit to the remaining digits. (340-18=322) Repeat the process: take 2 from 322 and multiply it by 2 (2*2=4). Subtract the doubled digit to the remaining number (32-4 28) 28 is divisible by 7, so |adv=Sort the numbers in blocks of three from right to left. Then, add the first group from the right, subtract the second group, then add the third, subtract the fourth, and so on. This is called the alternating sum of three. If the result is the multiple of 7, then the number is divisible by 7. |advex=Is 1,702,906,247 divisible by 7? First, group the numbers into blocks of three: 247, 906, 702, 1. Then, form the alternating sum: 247 - 906 + 702 - 1 = 42 Examine the results. Since 42 = 7 * 6, 42 is divisible by 7, thus 1,702,906,247 is, too. }} |simpex=Is 14625 divisible by 9? Add all the digits together: 1 + 4 + 6 + 2 + 5 = 18 18 is divisible by 9, so 14625 is, too. }} Divisibility of Numbers between 11 and 20 }} 56 is divisible by 7. Therefore, }} Divisibility of Numbers between 21 and 30 As 73,857 is divisible by both 3 and 7, 73,857 is divisible by 21. |adv=Alternatively, take the last digit of the number, multiply it by two, and then subtract it from the remaining digits of the numbers. Repeat the process until the result can be easily identified. |advex=To be filled up }} , so 33,242 is divisible by 22. }} 52 is divisible by 13. Therefore, }} 35 is divisible by 7. Therefore, }} Divisibility of Numbers between 31 and 40 Divisibility of Numbers between 41 and 50 Divisibility of Numbers between 51 and 60 Divisibility of Numbers between 61 and 70 Divisibility of Numbers between 71 and 80 Divisibility of Numbers between 81 and 90 Divisibility of Numbers between 91 and 100 Divisibility of Numbers between 101 and 110 Divisibility of Numbers between 111 and 120 |} Techinical Divisibility of Number Information Below lists down all the possible methods. The methods recommended will be bolded and displayed in blue text. Prime numbers from 2 ~ 100 |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= |trimleft=3 (multiply the first digit by 3, and then shift it 2 digits to the right, and add.) }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} Category: Important Pages